Let X,Y,Z⊆U. If n(U)=82, n(X)=24, n(Y)=32, n(Z)=33, n(X∩Y)=11, n(X∩Z)=7, n(Y∩Z)=10, and n(X∩Y∩Z)=3, find n(X′∩(Y∪Z′))

Answer 1

Use VENN DIAGRAM with 3 circles that overlap

X and Y and Z = 3

X and Y only not z = 8

X and Y = 11

X and Z only not Y = 4

X and Z = 7

Y and Z only not X = 7

Y and Z = 10

X only, not Y nor Z = 9

Y only, not Z nor x = 14

z only , not y nor x = 19

18 are NOT in X, nor Y, nor Z